Inelastic and elastic collision rates for triplet states of ultracold strontium

We report measurement of the inelastic and elastic collision rates for ${}^{88}\text{S}\text{r}$ atoms in the $\left(5s5p\right){{}^{3}P}_0$ state in a crossed-beam optical dipole trap. Since the $\left(5s5p\right){{}^{3}P}_0$ state is the lowest level of the triplet manifold, large loss rates indicate the importance of principle-quantum-number-changing collisions at short range. We also provide an estimate of the collisional loss rates for the $\left(5s5p\right){{}^{3}P}_2$ state. Large loss-rate coefficients for both states indicate that evaporative cooling toward quantum degeneracy in these systems is unlikely to be successful.

Figure 1

(Color online) Strontium atomic levels. Decay rates $\left({\text{s}}^{-1}\right)$ and excitation wavelengths are given for selected transitions. Laser light used for the experiment is indicated by solid lines. Dashed lines indicate transitions that are only made due to spontaneous decay. All levels with energy below $43000\text{K}$ are shown. The energy of the ${{}^{3}S}_1$ state is $41780.5\text{K}$. The inset gives the energy splittings of the metastable ${{}^{3}P}_J$ levels.

Figure 2

(Color online) Timing diagram for measuring metastable collision dynamics. Note the breaks in the time axis. Simultaneous application of the 688 and 689 nm lasers populates the metastable triplet levels. A strong 461 nm beam applied after the initial optical pumping ensures that no atoms remain in the ${{}^{1}S}_0$ state. For measuring ${{}^{3}P}_0$ dynamics and to keep the ${{}^{3}P}_2$ level unpopulated, the $3\mu \text{m}$ laser is on the entire time, and the 679 nm is pulsed on to repump the ${{}^{3}P}_0$ atoms to the ground state. For measuring ${{}^{3}P}_2$ dynamics, the timing of these two lasers is interchanged as indicated in the timing labeling.

Figure 3

(Color online) Left: number of trapped atoms as a function of time for studies of the ${{}^{3}P}_0$ state. Two-body fits allowing for one- and two-body losses using Eq. (1) and the numerical simulation described in the text are identical. The statistical uncertainties in the two-body loss-rate constant, $\beta =18\pm 3\times {10}^{-18}{\text{m}}^3/\text{s}$, and one-body loss rate, $\Gamma =1.4\pm 0.9{\text{s}}^{-1}$, are dominated by correlation between the parameters, but $\beta$ is determined much better than systematic uncertainties described in the text and is the dominant loss mechanism. The one-body fit sets $\beta =0$ and is not a good description of the data. The observed value for $\Gamma$ is consistent with the decay rate for ${{}^{1}S}_0$ atoms, which is dominated by background gas collisions. Right: temperature evolution of the trapped sample. The fit is from the numerical simulation. The ODT trap depth resulting from symmetric saddle points located approximately along the horizontal axes ($x$ and $z$) is $U_{trap}/k_B=20\mu \text{K}$. The potential barrier for escape along the vertical $\left(y\right)$ direction is $30\mu \text{K}$.

Figure 4

(Color online) Two-body decay rate measurements for the ${{}^{3}P}_0$ state. The solid line is ${\beta }_{el}=\sigma \overline{v}\sqrt{2}$, where $\sigma =8\pi a^2$, $\left|a\right|=100a_0$, and $\overline{v}=\sqrt{8k_{B}T/\pi m}$.